On the scalability of hypergraph models for sparse matrix partitioning

Bora Uçar (1, 2) , Umit V. Catalyurek (3)

1 GRAAL - Algorithms and Scheduling for Distributed Heterogeneous Platforms
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 Department of Biomedical Informatics [Columbus]

We investigate the scalability of the hypergraph-based sparse matrix partitioning methods with respect to the increasing sizes of matrices and number of nonzeros. We propose a method to rowwise partition the matrices that correspond to the discretization of two-dimensional domains with the five-point stencil. The proposed method obtains perfect load balance and achieves very good total communication volume. We investigate the behaviour of the hypergraph-based rowwise partitioning method with respect to the proposed method, in an attempt to understand how scalable the former method is. In another set of experiments, we work on general sparse matrices under different scenarios to understand the scalability of various hypergraph-based one- and two-dimensional matrix partitioning methods.

Keywords: Matrix partitioning; Hypergraph partitioning; Sparse matrix-vector multiplication.; Sparse matrix-vector multiplication

Domains: Computer Science [cs]; Distributed, Parallel, and Cluster Computing [cs.DC]; Mathematics [math]; Combinatorics [math.CO]

Bora Uçar, Umit V. Catalyurek. On the scalability of hypergraph models for sparse matrix partitioning. 18th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP 2010), IEEE, Feb 2010, Pisa, Italy. pp.593-600, ⟨10.1109/PDP.2010.92⟩. ⟨ensl-00529088⟩